Bellerin, 23, went down unchallenged during the second half of Arsenal’s 2-0 victory at the Emirates on Saturday and was carried off on a stretcher.
The 23-year-old was making his first start since mid-December, having overcome a calf problem, but will now miss the remainder of the season, and possibly the start of the 2019/20 campaign.
“Further to the injury sustained during our match against Chelsea on Saturday, we can confirm that Hector has ruptured the anterior cruciate ligament of his left knee,” the club said in a statement on its website.
“Hector will undergo surgery to repair this in the coming days. The rehabilitation process is expected to take between six to nine months and therefore rules Hector out of action for the remainder of this season.
“Everyone at the club will now be working as hard as we can to ensure Hector is back on the pitch as soon as possible next season.”
Head coach Unai Emery said after the Chelsea game that Bellerin could have an “important” injury and that the initial prognosis was not positive.
Bellerin’s Arsenal team-mate Rob Holding suffered a similar injury in a 2-2 draw at Manchester United on December 5.
While the January transfer window would allow Arsenal to bring in cover at right-back, Emery does have options in Stephan Lichtsteiner, Ainsley Maitland-Niles and Carl Jenkinson, who was expected to be allowed to leave the Emirates Stadium this month before Bellerin’s setback.
Arsenal are fifth in the Premier League, three points behind fourth-placed Chelsea.